July 3rd, 2017, 03:40 PM  #1 
Senior Member Joined: Jul 2016 From: USA Posts: 108 Thanks: 13  f'(x) = 4*sqrt(f(x))
f'(x) = 4*sqrt(f(x)) [derivative with respect to x of f(x) = 4 * squareroot of f(x)] Does anyone know how to solve equations like this? The goal is to solve for f(x). I run into equations like this so often and always get stuck. 
July 3rd, 2017, 04:05 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,857 Thanks: 2230 Math Focus: Mainly analysis and algebra 
Separation of variables. $$y'=4\sqrt{y} \implies \int y^{\frac12} \, \mathrm dy = 4\int \mathrm dx$$ Last edited by v8archie; July 3rd, 2017 at 04:07 PM. 

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